# Games and Puzzles

### 3-Dimensional Tic-Tac-Toe

There are lots of Tic-Tac-Toe (Noughts and Crosses, whatever) games and strategies out there, but not many truly 3-dimensional games.  There are variations which require players to stack a piece on top of a previously played piece, which changes the game.  There are games made with a 4-by-4-by-4 array, which eliminates the problem of the first player always winning on the third move, as happens with a 3 by 3 by 3 array.  And there are virtual games and formats to play on a single sheet of paper.  But there aren’t many ways to play Tic-Tac-Toe in three dimensions the same way it’s played in two.

Here’s a solution.  This is a 3 by 3 by 3 array that allows players to play in any space in any order.  The one rule change is that the center space is not allowed on the very first move.

The first player will always win even with that rule change, however, as long as the game ends with the first “three in a row.”  So it doesn’t.  Players continue playing...

### Towers of Hanoi

I understand the origins of the Towers of Hanoi is derived from Southeast Asian creation lore.  The Creator is playing the game with 64 disks instead of 8.  When it's done, the world comes to an end.

A more manageable version includes 8 disks instead of 64.  But it's made much more bite-sized by having students try it with 2 disks, then 3, and then with greater numbers.

The rules are as follows...